Noise sensitivity of phase-synchronization time in stochastic resonance: theory and experiment

Recent numerical and heuristic arguments have revealed that the average phase-synchronization time between the input and the output associated with stochastic resonance is highly sensitive to noise variation. In particular there is evidence that this average time exhibits a cusplike behavior as the noise strength varies through the optimal value. Here we present an explicit formula for the average phase-synchronization time in terms of the phase diffusion coefficient and the average frequency difference between the input and the output signals. We also provide experimental evidence for the cusplike behavior by using a bistable microelectronic-circuit system.